Mathematical Concepts in Organic Chemistry

Degree-Based Topological Indices

“…Before this, we need to recall a few concepts from chemical graph theory. 12,13 Under "molecular graph" we understand a simple graph, representing the carbon-atom skeleton of an organic molecule (usually, of a hydrocarbon). Thus, the vertices of a molecular graph represent the carbon atoms, and its edges the carbon-carbon bonds.…”

Atom Bond Connectivity Indices of Kragujevac Trees (Kgd,k)

“…Mathematical chemistry is a branch of theoretical chemistry using mathematical methods to discuss and predict molecular properties without necessarily referring to quantum mechanics [1,15,22]. Chemical graph theory is a branch of mathematical chemistry which applies graph theory in mathematical modeling of chemical phenomena [8].…”

Enumerating independent vertex sets in grid graphs

“…The Merrifield-Simmons index and the Hosoya index of a graph, respectively introduced by Merrifield and Simmons [11,12,13] and by Hosoya [8], are two prominent examples of topological indices for the study of the relation between molecular structure and physical/chemical properties of certain hydrocarbon compound, such as the correlation with boiling points [5]. An independent set of vertices/edges of a graph G is a set of which no two vertices of the set are connected by a single edge.…”

“…For example, among trees with the same number of vertices, Prodinger and Tichy [17] proved that the star maximizes the Merrifield-Simmons index, while the path minimizes it. The situation for the Hosoya index is absolutely opposite; the star minimizes the Hosoya index, while the path maximizes it [5]. A good summary of results for extremal graphs of various types can be found in a survey paper [18].…”